S.H.
Try the books:
1) Have A New Kid By Friday by Leman
2) How to Talk So Kids Will Listen and Listen So Kids Will talk.
You can read about it and the reviews of both these books, on Amazon.
MANY MANY kids, behave better with others. And with Mom, not. Because they, although it seems contrary, they are more comfortable with you so they let it all hang out.
Try also teaching your kids HOW to communicate. Kids this age, don't even know how to have a 'conversation.' So teach them.
Role Play with them, give them examples and what sentences/words they can use.
Emphasize, "TEAMWORK". My son likes that.
Also, I used the "Redo' approach.
Meaning, when a kid is being yucky... tell them "Redo that." It gives them a chance, to redo what they did, in a nicer way. That works with my son, too. Then, if they do not/cannot redo or correct their response, THEN do whatever punishment you deem fit.
Also teach them what a sibling is. But siblings DO fight. Even the best of siblings. But teach them what "FAMILY" means, it means watching each others back and helping....
Try having them, each day, think of 3 things that they did that was nice... or thoughtful. So that they get used to thinking of someone else and empathy.. ... instead of thinking of themselves.
Also, ask them, to each day (you all sit together with them), ask them what they did for MOMMY, to help and to help the FAMILY and the household.
Then, make a smiley face, for them, on a piece of paper.
ALSO though, emphasize that they 'try their best." Not that is HAS TO be 'Perfect"... but that they are trying. THAT is good.
So they can be commended on that.
Also this is a great article on how to talk & not talk to your kids:
http://nymag.com/news/features/27840/
ALSO (and I did this with my eldest child), but EXPLAIN to your Eldest, about child development, in simple terms she can understand. So THAT, she will understand that her 2.5 year old sibling, CANNOT do things like she can or understand things like she can. My daughter was about 4 years old when I had my 2nd child. I explained to her each month , about how her brother is changing and his development... and that at his age, he is younger and not the same as her, in ability etc. THAT helped my daughter, have more understanding for her little brother. I still do that with her... my son is now 4 years old. So now, my daughter CAN understand, how her younger sibling, is per his age.
all the best,
Susan